for \(p\) -almost every curve \(\gamma \colon [0,\ell _\gamma ]\rightarrow X\) ; that is, there exists a non-negative Borel function
\(\rho \in L^p_{\mathrm {loc}}(X;d\mu )\)  such that
\(\int _\gamma \rho \,ds=\infty \)  whenever (REF ) does not hold or is not defined.
For a function \(u\in L^p(X;d\mu )\) , we denote by \(\mathcal {D}^{p}(u)\) 
the set of all \(p\) -weak upper gradients \(g\in L^p(X;d\mu )\)  of \(u\) .
We remark that \(\mathcal {D}^p(u)\)  can be empty.
See [1]} and [2]}
for detailed treatments of \(p\) -weak upper gradients.
